Students will learn about pressure and solving pressure problems in the context of fluids.

Key Equations

Guidance

The
pressure
of a fluid is a measure of the forces exerted by a large number of molecules when they collide and bounce off its boundary. The unit of pressure is the Pascal (Pa).

In a fluid at rest, pressure increases linearly with depth – this is due to the weight of the water above it.

Pascal’s Principle
reminds us that, for a fluid of uniform pressure, the force exerted on a small area in contact with the fluid will be smaller than the force exerted on a large area. Thus, a small force applied to a small area in a fluid can create a large force on a larger area. This is the principle behind hydraulic machinery.

Liquids obey a
continuity equation
which is based on the fact that liquids are very difficult to compress. This means that the total volume of a fluid will remain constant in most situations. Imagine trying to compress a filled water balloon!

Example 1

A weather balloon is ascending through the atmosphere. If the density of air is 1.2 kg/m
3
and atmospheric pressure at sea level is 101.3 kPa, then what is the pressure on the balloon at (a) 100 m above the ground, (b) 500 m above the ground, and (c) 1000 m above the ground?

Solution

For all parts of these problems, we'll be using the equation for pressure given above where the atmospheric pressure at sea level is P
o
.

(a):

(b):

(c):

Watch this Explanation

Time for Practice

A
car is being lifted by a hydraulic jack attached to a flat plate. Underneath the plate is a pipe with radius
.

If there is no net force on the car, calculate the pressure in the pipe.

The other end of the pipe has a radius of
. How much force must be exerted at this end?

To generate an upward acceleration for the car of
, how much force must be applied to the small end of the pipe?

A SCUBA diver descends deep into the ocean. Calculate the water pressure at each of the following depths.

Ouch! You stepped on my foot! That is, you put a force of
in an area of
on the tops of my feet!